1. Field of the Invention
The present invention generally relates to a color converting method and, more particularly, to the color converting method performed by a color reading apparatus for converting red (R), green (G) and blue (B) color data, which are light data, into yellow (Y), magenta (M) and cyan (C) color data utilizable for the preparation of an ink.
2. Description of the Prior Art
A color light can be expressed by a combination of respective values of R, G and B. FIG. 4 illustrates a diagram in which those values of R, G and B are depicted in a three-dimensional representation.
Referring to FIG. 4, the color C(C) is represented by one point lying in the system of rectangular coordinates defined by R, G and B, the coordinate of which is (R, G, B). This can be considered a vector of R, G and B components.
The length of the vector in this three-dimensional representation describes the brightness of the color light and is converted with a change in color. In other words, a change in color means only a change in the direction of the vector.
FIG. 5 is a diagram used to explain the system of coordinates descriptive of the chromaticity of the color light. The origin represented by R=G=B=0 is the point at which the energy of the color light is zero and, thus, the brightness is zero.
Since the white color Cw(W), which is taken as a reference, is expressed by R=G=B, the vector thereof extends outwardly from a plane (unitary plane). It forms a part of the equilateral triangle having its vertices lying at respective coordinates (1, 0, 0), (0, 1, 0) and (0, 0, 1) as shown in FIG. 5.
Since, as hereinbefore described, the difference in color in the three-dimensional representation is the difference in direction of the vector, and if only the color is taken into consideration, the color C can be expressed by the point of intersection in the system of coordinates between the planes of the equilateral triangle and the color vector. If the coordinates of this point of intersection are expressed by (r, g, b), the equation of the color in that point will be as follows. EQU c(C)=r(R)+g(G)+b(B) (1)
And, EQU r=R/.SIGMA., g=G/.SIGMA., b=B/.SIGMA.
wherein .SIGMA. represents a certain constant.
The equation which gives a point (x, y, z) on the plane can be expressed as follows, if respective points at which the plane intersect the x-, y- and z-axes are expressed by a, b and c. EQU x/a+y/b+z/c=1
Therefore, in the unitary plane shown in FIG. 5, a=b=c=1, or EQU r+g+b=1 (2).
This occurs if x, y and z are rewritten as r, g and b, respectively. Since the equation (2) can be rewritten to read; EQU R/.SIGMA.+G/.SIGMA.+B/.SIGMA.=1, (3)
then, EQU .SIGMA.=R+G+B.
Therefore; EQU r=R/(R+G+B), g=G/(R+G+B), b=B/(R+G+B)
Hereinafter, the relationship between the light R, G and B and the pigments Y, M and C will be discussed.
As is the case with the light R, G and B, the pigments Y, M and C can also be expressed in a three-dimensional representation. Considering the possibility in which arbitrarily chosen points in the system of R, G and B coordinates in a color space are converted into a system of Y, M and C coordinates, the relationship between Y, M and C and R, G and B can be expressed as follows. ##EQU1## Assuming that ##EQU2## is expressed by A, ##EQU3##
However, as shown in FIG. 3, Y and B, M and G, and C and R are chromaticitically opposite to each other. In other words, if r+g+b=1 represents a white color in the case of the light, y+m+c=-1 represents a black color in the case of the pigment.
Referring to FIG. 3, it can be understood that the light R+G of r.multidot.1/3+g.multidot.1/3 in chromaticity is necessary in order for the pigment Y to give a chromaticity of -y.multidot.1/3 In other words, the light having a chromaticity corresponding to the chromaticity of Y is R+G.
In view of the foregoing, if the terms of B, G and R corresponding to Y, M and C in the equation (4) are rendered to be (R+G), (R+B) and (G+B), respectively, the value of a matrix coefficient A can be reduced. Further, the color conversion from the light R, G and B into the pigments Y, M and C, respectively, can be accurately achieved. Therefor, rewriting the equation (4) results in: ##EQU4## and, in view of R+G+B=1, ##EQU5##
According to the prior art color reading apparatus, the total color conversion has been carried out by the use of the same A' (matrix coefficient).
However, it has been found that the total color conversion with the use of the same matrix coefficient often results in uneven color reproduction, some exhibiting a good color reproducibility while others do not.